A LIKELIHOOD APPROACH TO HLA SEROLOGY

SUMMARY A likelihood approach to HLA serology has been developed in which the aim is not to define a recognition set for a serum but to describe the serum's ability to react with each and every antigen in the test cells, this ability being quantified in terms of the probability of a positive reaction. For a given set of probabilities, one for each antigen, it is possible to derive the probability of the observed set of reactions (the likelihood of the set of probabilities). The maximum possible value of the likelihood for any possible combination of the probability set can then be sought, but this requires a maximization of likelihood with respect to 60–100 independent parameters. Theoretical considerations of the shape of the likelihood surface prove that, in this particular case, this is a feasible proposition. This approach allows the recognition of three groups of antigens: those for which there is considerable evidence of a specificity, those for which there is either no specificity or a very weak specificity, and those for which there is insufficient evidence on which to base a conclusion. The existence of a specificity can be tested using a log likelihood ratio as a statistic, but the usual assumption of a χ2 distribution of this statistic cannot automatically be made in this situation. Therefore, the distribution is estimated by simulation. A serologist using this approach would receive considerably more information as to the serum's reaction patterns and valid statistics for the existence, or not, of a specificity.